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Simulation of Microbunching Instability in LCLS with a Laser Heater

This research presents a detailed simulation of microbunching instability in the Linac Coherent Light Source (LCLS) using a laser heater. The study employs a Longitudinal Space Charge (LSC) model implemented in ELEGANT to analyze density and energy modulation phenomena. Key findings highlight the significance of LSC in photoinjectors and downstream beamlines, exploring both cases with and without a laser heater. Results demonstrate effective modeling for stability studies, showcasing the integration of analytical techniques and simulations to improve accuracy in high-frequency microbunching scenarios.

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Simulation of Microbunching Instability in LCLS with a Laser Heater

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  1. Simulation of Microbunching Instability in LCLS with Laser-HeaterJuhao Wu, M. Borland (ANL), P. Emma, Z. Huang, C. Limborg, G. Stupakov, J. Welch • Longitudinal Space Charge (LSC) modeling • Drift space and Accelerator cavity as test-bed for a LSC model • Implement of LSC model in ELEGANT • Simulation of microbunching instability (ELEGANT) • Without laser-heater • With laser-heater Juhao Wu, SLAC

  2. Motivation • What’s new?  LSC important in photoinjector and downstream beam line; (see Z. Huang’s talk) • PARMELA / ASTRA simulation time consuming for S2E; difficult for high-frequency microbunching (numerical noise); • Find simple, analytical LSC model, and implement it to ELEGANT for S2E instability study; • Starting point –- free-space 1-D model; (justification) • Transverse variation of the impedance  decoherence; small? 2-D? • Pipe wall  decoherence; small? • Test LSC model in simple element • Use such a LSC model for S2E instability study Juhao Wu, SLAC

  3. LSC Model (1-D) • Free space 1-D model: transverse uniform coasting beam with longitudinal density modulation (on-axis) • where, rb is the radius of the coasting beam; λ rb pancake beam pencil beam • For more realistic distribution  find an effective rb, and use the above impedance; • Radial-dependence of the impedance will increase energy spread and enhance damping; small? Juhao Wu, SLAC

  4. Space Charge Oscillation in a Coasting Beam • Distinguish: low energy case  high energy case; • Space charge oscillation becomes slow, when the electron energy becomes high; the residual density modulation is then ‘frozen’ in the downstream beam line. rb=0.5 mm, I0=100 A E = 12 MeV E = 6 MeV Juhao Wu, SLAC

  5. Two Quantities • The quantities we concern are density modulation, and energy modulation Heifets-Stupakov-Krinsky(PRST,2002); Huang-Kim(PRST,2002) (CSR) Density modulation Integral equation approach Energy modulation R56 Juhao Wu, SLAC

  6. Testing the LSC model • Analytical integral equation approach • Find an effective radius for realistic transverse distributions and use 1-D formula for LSC impedance; for parabolic & Gaussian • Generalize the momentum compaction function to treat acceleration in LINAC, and for drift space as well • Simulation • PARMELA • ASTRA • ELEGANT  Juhao Wu, SLAC

  7. Integral Equations Density modulation Energy Modulation: • Applicable for both accelerator cavity and drift space • Impedance for LSC Juhao Wu, SLAC

  8. Analytical Approach – Two Limits • Analytical integral equation approach – two limits • Density and energy modulation in a drift at distance s; • At a very large , plasma phase advance (s/c) << 1, •  “frozen,” energy modulation gets accumulated • (Saldin-Schneidmiller-Yurkov, TESLA-FEL-2003-02) • Integral equation approach deals the general evolution of the density and energy modulation  Juhao Wu, SLAC

  9. Analytical vs. ASTRA (energy modulation) • 3 meter drift without acceleration • In analytical approach: • Transverse beam size variation due to transverse space charge: included; • Slice energy spread increases: not included; • 1 keV resolution? Coasting beam vs. bunched beam? Juhao Wu, SLAC

  10. Analytical vs. ASTRA (density modulation) • 3 meter drift without acceleration Juhao Wu, SLAC

  11. Analytical vs. PARMELA (energy modulation) • Assume 10% initial density modulation at gun exit at 5.7 MeV; • After 67 cm drift + 2 accelerating structures (150 MeV in 7 m), LSC induced energy modulation; PARMELA simulation Analytical approach Juhao Wu, SLAC

  12. S2E Simulation • LSC model • Analytical approach agrees with PARMELA / ASTRA simulation; • Wall shielding effect is small as long as (typical in our study); • Free space calculation overestimates the results (10 – 20%); • Radial-dependence and the shielding effect  decoherence; (effect looks to be small) • Free space 1-D LSC impedance with effective radius has been implemented in ELEGANT; • S2E simulation • Injector simulation with PARMELA / ASTRA (see C. Limborg’s talk); • downstream simulations ELEGANT with LSC model(CSR, ISR, Wake etc. are all included) Juhao Wu, SLAC

  13. Comparison with ELEGANT • Free space 1-D LSC model with effective radius • Example with acceleration: current modulation at different wavelength I=100 A, rb=0.5 mm, E0=5.5 MeV, Gradient: 7.5 MV/m --- 1 mm, --- 0.5 mm, --- 0.25 mm, --- 0.1 mm Elegant tracking Analytical calculation Juhao Wu, SLAC

  14. Simulation Details • Halton sequence (quiet start) particle generator • Based on PARMELA output file at E=135 MeV, with 200 k particles • Longitudinal phase space: keep correlation between t and p --- fit p(t), and also local energy spread p(t) • Multiply density modulation ( 1 %) • Transverse phase space: keep projected emittance • 6-D Quiet start to regenerate 2 million particles • Bins and Nyquist frequency --- typically choose bins to make the wavelength we study to be larger than 5 Nyquist wavelength • 2000 bins for initial 11.6 ps bunch • Nyquist wavelength is 3.48  m • We study wavelength longer than 20  m Juhao Wu, SLAC

  15. Simulation Details • Wake • Low-pass filter is essential to get stable results • Smoothing algorithms (e.g. Savitzky-Golay) is not helpful • Non-linear region • Synchrotron oscillation  rollover  harmonics • Low-pass filter is set to just allow the second harmonic Current form-factor Low-pass filter Impedance Juhao Wu, SLAC

  16. Simulation Details • Gain calculation (linear region) • Choose the central portion to do the analysis • Use polynomial fit to remove any gross variation • Use NAFF to find the modulation wavelength and the amplitude Juhao Wu, SLAC

  17. Phase space evolution along the beam line • Without laser-heater ( 1% initial density modulation at 30 m ) • Really bad • With matched laser-heater ( 1% initial density modulation at 30 m ) • Microbunching is effectively damped Juhao Wu, SLAC

  18. DE/E DE/E time (sec) time (sec) 510-5 510-5 30 mm injector output (135 MeV) 1% LCLS l0 = 30 mm NO HEATER

  19. DE/E DE/E time (sec) time (sec) 510-5 510-5 30 mm after DL1 dog-leg (135 MeV) LCLS l0 = 30 mm NO HEATER

  20. DE/E DE/E time (sec) time (sec) 110-3 110-3 30 mm before BC1 chicane (250 MeV) LCLS l0 = 30 mm NO HEATER

  21. DE/E DE/E time (sec) time (sec) 110-3 110-3 30/4.3 mm after BC1 chicane (250 MeV) LCLS l0 = 30 mm NO HEATER

  22. DE/E DE/E time (sec) time (sec) 510-4 510-4 30/4.3 mm before BC2 chicane (4.5 GeV) LCLS l0 = 30 mm NO HEATER

  23. DE/E DE/E time (sec) time (sec) 210-3 210-3 30/30 mm after BC2 chicane (4.5 GeV) LCLS l0 = 30 mm NO HEATER

  24. DE/E DE/E time (sec) time (sec) 110-3 110-3 0.09 % rms 30/30 mm before undulator (14 GeV) LCLS l0 = 30 mm NO HEATER

  25. DE/E DE/E time (sec) time (sec) 510-5 510-5 30 mm injector output (135 MeV) 1% LCLS l0 = 30 mm MATCHED HEATER

  26. DE/E DE/E time (sec) time (sec) 510-4 510-4 30 mm just after heater (135 MeV) LCLS l0 = 30 mm MATCHED HEATER

  27. DE/E DE/E time (sec) time (sec) 510-4 510-4 30 mm after DL1 dog-leg (135 MeV) LCLS l0 = 30 mm MATCHED HEATER

  28. DE/E DE/E time (sec) time (sec) 110-3 110-3 30 mm before BC1 chicane (250 MeV) LCLS l0 = 30 mm MATCHED HEATER

  29. DE/E DE/E time (sec) time (sec) 210-3 210-3 30/4.3 mm after BC1 chicane (250 MeV) LCLS l0 = 30 mm MATCHED HEATER

  30. DE/E DE/E time (sec) time (sec) 510-4 510-4 30/4.3 mm before BC2 chicane (4.5 GeV) LCLS l0 = 30 mm MATCHED HEATER

  31. DE/E DE/E time (sec) time (sec) 510-4 510-4 30/30 mm after BC2 chicane (4.5 GeV) LCLS l0 = 30 mm MATCHED HEATER

  32. DE/E DE/E time (sec) time (sec) 210-4 210-4 0.01% rms 30/30 mm before undulator (14 GeV) LCLS l0 = 30 mm MATCHED HEATER

  33. LCLS gain and slice energy spread End of BC2 Nonlinear region / Saturation 1%, 30m Undulator entrance Juhao Wu, SLAC

  34. Discussion and Conclusion • Instability not tolerable without laser-heater for  < 200 -- 300 m with about  1% density modulation after injector; • Laser-heater is quite effective and a fairly simple and prudent addition to LCLS; • Injector modulation study also important, no large damping is found to confidently eliminate heater. (see C. Limborg’s talk) Juhao Wu, SLAC

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